Recursive problem

When the problem is equilibrated with the ratio of variable, clauses classified as hard, the possible solution bufurcate in exponential ratio.
For every variable, one option 0 or 1 bifurcates at least in two paths where 1/r of both paths are completely independent. The reason is you will have to explore 1/r  subset of solutions in one bifurcation totally independent from the other option.

In hard problems where clauses are rightly abundant and intermixed and solutions are a few, you are forced to explore (1+1/r)^num-vars different paths all completely independent.

That is one does not tell you anything about the other, still if is hard, probably only a few have solution. So it points to NP not P, at least without quantum computers domain.

It is true that you can apply some heuristics to search first the most promising paths, but if the few solutions are in different sides and well distributed, the mixed signals does not let you focus in one, but in the middle path that lets to nowhere. (In hard problems of course).

Example of heuristic, how many clauses and its size are left in every option. Less, looks better for a global minimum, but we have different global minimums, and it looks we want to go to all at a single ride, but they are completely at other extremes between them.

What would be lovely? Have a problem and that we could choose any unset variable and ask: if i set this to 0, will it be solvable? In case both said yes 0 and 1 would stop searching for one path just for the sake of focusing on one solution.